Re: [理工] 線代問題
※ 引述《king111 (.....)》之銘言：
: 請問有人可以幫解這三題嗎 我想很久還是想不出來... 謝謝
: Let T:R4→R3 be a linear transformation defined by
: T(x,y,z,t)=(x-2y+z-t,3x-2z+3t,5x-4y+t)
: Find the value of w if(1,5,w)屬於Im T,the image of T
Im(T) = span{ T(e1), T(e2), T(e3), T(e4)}
= span{(1,3,5),(-2,0,-4),(1,-2,0),(-1,3,1)}
=> 刪去線性相依的向量(-1,3,1)
∴Im(T)的一組基底為 { (1,3,5), (-2,0,-4), (1,-2,0) }
∴此基底生成(1,5,w)
=> (1,5,w) = a (1,3,5) + b (-2,0,-4) + c (1,-2,0)
a-2b+c = 1 ---- A
=> 3a -2c = 5 ---- B
5a -4b = w ---- C
=> 2A+B = C
∴w = 7
其實這題可以直接用看的,不需要這麼麻煩( ′-`)y-～
: Give an example of a martrix A with the propety that Ax=b has a solution for
: b=(1,-3,1) and has no solution for b=(0,1,2).
就...隨便找吧
找個一.三列相等的矩陣
[1 2 1]
取 A= [3 4 5]
[1 2 1]
: If u,v,and w are nonzero vectors and r is a scalar,prove that
: (a) (ru)v = r(uv)
: (b) (u+v)w = uw + vw
這好難..我不會證..Orz
請求高手幫忙
有錯誤請指正,感謝
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